Probing dark matter and dark energy through gravitational time advancement

The expression of gravitational time advancement (negative time delay) for particles with non-zero mass in Schwarzschild geometry has been obtained. The influences of the gravitational field that describes the observed rotation curves of spiral galaxies and that of dark energy (in the form of cosmological constant) on time advancement of particles have also been studied. The present findings suggest that in presence of dark matter gravitational field the time advancement may take place irrespective of gravitational field of the observer, unlike the case of pure Schwarzschild geometry where gravitational time advancement takes place only when the observer is situated at stronger gravitational field compare to the gravitational field encountered by the particle during its journey. When applied to the well known case of SN 1987a, it is found that the net time delay of a photon/gravitational wave is much smaller than quoted in the literature. In the presence of dark matter field, the photon and neutrinos from SN 1987a should have been suffered gravitational time advancement rather than the delay.